{"paper":{"title":"Certification of inequalities involving transcendental functions: combining SDP and max-plus approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benjamin Werner, St\\'ephane Gaubert, Victor Magron, Xavier Allamigeon","submitted_at":"2013-07-26T11:41:05Z","abstract_excerpt":"We consider the problem of certifying an inequality of the form $f(x)\\geq 0$, $\\forall x\\in K$, where $f$ is a multivariate transcendental function, and $K$ is a compact semialgebraic set. We introduce a certification method, combining semialgebraic optimization and max-plus approximation. We assume that $f$ is given by a syntaxic tree, the constituents of which involve semialgebraic operations as well as some transcendental functions like $\\cos$, $\\sin$, $\\exp$, etc. We bound some of these constituents by suprema or infima of quadratic forms (max-plus approximation method, initially introduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7002","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}